Nonlinear H∞ control of robotic manipulator

H_∞ control theory for nonlinear systems has been developed, which is based on the concept of energy dissipation. A nonlinear H_∞ controller using energy dissipation is designed in the sense of L₂-gain attenuation from a disturbance to performance and it is essential to find the solution of the Hamilton Jacobi (HJ) equation (or inequality) for application. However, it is difficult to obtain its solution in general. In this paper, the robot dynamics is transformed to a affine form to express the HJ inequality as a more tractable form, i.e., a nonlinear matrix inequality (NLMI), and its approximated solution is obtained from the fact that the terms in matrices which describe robot manipulator can be bounded